4.Something given or done in return for a favor, message, etc.Smollett.

5.A declaration or avowal of one's own act, to give it legal validity; as, the acknowledgment of a deed before a proper officer. Also, the certificate of the officer attesting such declaration.
Acknowledgment money, in some parts of England, a sum paid by copyhold tenants, on the death of their landlords, as an acknowledgment of their new lords.
Cowell.Syn. -- Confession; concession; recognition; admission; avowal; recognizance.